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Romania National Olympiad
1999 Romania National Olympiad
2
a^2 +b^2 +c^2 never prime 1999 Romania NMO VII p3
a^2 +b^2 +c^2 never prime 1999 Romania NMO VII p3
Source:
August 14, 2024
number theory
prime
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be non zero integers,
a
≠
c
a\ne c
a
=
c
such that
a
c
=
a
2
+
b
2
c
2
+
b
2
\frac{a}{c}=\frac{a^2+b^2}{c^2+b^2}
c
a
=
c
2
+
b
2
a
2
+
b
2
Prove that
a
2
+
b
2
+
c
2
a^2 +b^2 +c^2
a
2
+
b
2
+
c
2
cannot be a prime number.
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